On the relations and differences between Popper dimension, exclusion dimension and VC-Dimension

Seldin, Yevgeny & Schölkopf, Bernhard (2013) On the relations and differences between Popper dimension, exclusion dimension and VC-Dimension. In Schölkopf, Bernhard, Luo, Zhiyuan, & Vovk, Vladimir (Eds.) Empirical Inference : Festschrift in Honor of Vladimir N. Vapnik. Springer, Heidelberg.

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Abstract

A high-level relationPopper dimension—( Exclusion dimension—( VC dimension—( between Karl Popper’s ideas on “falsifiability of scientific theories” and the notion of “overfitting”Overfitting in statistical learning theory can be easily traced. However, it was pointed out that at the level of technical details the two concepts are significantly different. One possible explanation that we suggest is that the process of falsification is an active process, whereas statistical learning theory is mainly concerned with supervised learningSupervised learning, which is a passive process of learning from examples arriving from a stationary distribution. We show that concepts that are closer (although still distant) to Karl Popper’s definitions of falsifiability can be found in the domain of learning using membership queries, and derive relations between Popper’s dimension, exclusion dimension, and the VC-dimensionVC dimension.

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ID Code: 70842
Item Type: Book Chapter
DOI: 10.1007/978-3-642-41136-6_6
ISBN: 9783642411359
Divisions: Current > QUT Faculties and Divisions > Science & Engineering Faculty
Deposited On: 01 May 2014 01:15
Last Modified: 25 Dec 2015 17:16

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